new user and my math problem

Hi
My name is Anja and I joined here as I am not sure how to progress with a data/math problem I have and was hoping to find some help. I work as an air quality researcher and am not a mathematician and probably can join in here more with questions than answers (sorry).
I have a set of results and according to literature the data should fit the following equation: ATN= -100 ln (α + (1-α) exp(-σ [BC])). I have a set of ATN and corresponding BC measurements but need to determine best fit α and σ. What's the best way to go about it?